Haha I was actually going to say that in my original post until I noticed something was just not right about that black saddle.
The adjustment part is actually welded to the black seat; i.e. the black seat doesn't have rails.

Considering the wide availability of modern cheapie 1 piece seatposts from china, OP might be able to get away with one provided he finds the size.
Otherwise what squidpuppet said.